Differentiability...

1) (a doubt) If f(x) = x²sin 1x , xâ‰ 0
x, x=0

then find f'(0) if it exists...

2) (not a doubt) Given f(x) = |x| and g(x) = |x³|. Do the derivatives, f(0) and g'(0) exist? Explain!! :P

please give detailed solution for the first one only.[1]

1 Answers

1) f'(0) = lim_{Î”xâ†’0} f(0+Î”x)-f(0)Î”x = lim_{Î”xâ†’0} Î”x sin1Î”x = 0
The last equality follows from Sandwich principle.

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